This application proposes a phase Ib trial to develop rapamycin (RAPA), a mammalian target of rapamycin (mTOR) inhibitor, as an anti-tumor agent with pharmacodynamic (PD) analysis. RAPA is currently an FDA approved drug in the treatment of renal allograft rejection. RAPA analogues are being studied as cancer therapies since mTOR is recognized as a relevant target in several cancer types. Yet there has never been any study of RAPA in this setting. The process of developing an FDA approved drug for a different indication is normally much more rapid than approval of investigational agents and thus RAPA could be available for use in cancer patients sooner than its analogues. The United States patent for RAPA in malignant disease has expired and thus there is no proprietary protection for developing the agent dampening commercial interest. RAPA is readily available, has been well-studied in allo-transplant patients, was the first recognized mTOR inhibitor, and demonstrates efficacy in pre-clinical cancer models. The aims of this study are to find the maximum tolerated dose (MTD), observed toxicities, dose limiting toxicities, and model a PD marker of RAPA administered to patients with advanced malignancies. A dose-effect relationship will be defined between RAPA and inhibition of the known RAPA/mTOR dependent phosphorylation at threonine 389 of p70 S6 kinase (S6K). The relationship between suppression of S6K phosphorylation and RAPA blood levels will also be determined. RAPA will be administered to successive cohorts of patients in escalating doses on a once-weekly intermittent schedule. The schedule was chosen to avoid immunosuppression associated with daily RAPA administration. Once the MTD is determined, there will be an expansion at the dose(s) that maximally inhibit phospho-S6K in the phase Ib portion of the trial. At the conclusion of the trial RAPA toxicity and effect on p-S6K will be defined over a range of doses as well as the MTD for use in future studies that will develop this agent.